A random variable X had probability distribution given by Pr

A random variable X had probability distribution given by

Pr(X = x) ={c(6 -x) x = 1; 2; 3; 4; 5

                  { 0 otherwise

where c is a constant. Determine

(A) The value of c

(B) Pr(X <= 2)

Solution

(A)

c( 5*1 + 4*2 + 3*3 + 2*4+ 1*5) = 1

=> c = 1 / 35

(B)

Pr(X <= 2) = Pr(X=1) +Pr(X=2)

                = 1/35 * ( 5*1 + 4*2)

                 = 1/35 * 13

                 = 0.37 Answer